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Integrated Pearson family and orthogonality of the Rodrigues polynomials: A review including new results and an alternative classification of the Pearson system

Volume 42 / 2015

G. Afendras, N. Papadatos Applicationes Mathematicae 42 (2015), 231-267 MSC: Primary 62E15, 60E05; Secondary 62-00. DOI: 10.4064/am42-2-9


An alternative classification of the Pearson family of probability densities is related to the orthogonality of the corresponding Rodrigues polynomials. This leads to a subset of the ordinary Pearson system, the so-called Integrated Pearson Family. Basic properties of this family are discussed and reviewed, and some new results are presented. A detailed comparison between the Integrated Pearson Family and the ordinary Pearson system is presented, including an algorithm that enables one to decide whether a given Pearson density belongs, or not, to the integrated system. Recurrences between the derivatives of the corresponding orthonormal polynomials are also given.


  • G. AfendrasDepartment of Biostatistics
    University at Buffalo
    Buffalo, NY 14214, U.S.A.
  • N. PapadatosDepartment of Mathematics
    Section of Statistics and O.R.
    University of Athens
    157 84 Athens, Greece

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